1. Field of the Invention
The present invention relates to a Multiple Input Multiple Output (MIMO) system supporting a spatial multiplexing scheme. More particularly, the present invention relates to an apparatus and method for parallel symbol cancellation for Maximum Likelihood (ML) detection.
2. Description of the Related Art
In a Multiple Input Multiple Output (MIMO) System, each of the transmitting/receiving ends utilize multiple antennas. The MIMO system advantageously increases a transmission capability when compared with a Single Input Single Output (SISO) system that uses a single transmitting/receiving antenna, particularly when the MIMO system uses a spatial multiplexing scheme for simultaneously transmitting a plurality of signals through a multiple antenna.
As illustrated in FIG. 1, in a MIMO system having two transmitting antennas and two receiving antennas, if the transmitting end transmits a transmitted symbol vector (x=[d1d2]T), the receiving end receives the transmitted signal vector. The received signal vector is expressed in Equation (1) below:
                    r        =                                            H              ·              x                        +            n                    =                                                    [                                                                                                    h                        11                                                                                                            h                        21                                                                                                                                                h                        12                                                                                                            h                        22                                                                                            ]                            ·                              [                                                                                                    d                        1                                                                                                                                                d                        2                                                                                            ]                                      +                          [                                                                                          n                      1                                                                                                                                  n                      2                                                                                  ]                                                          (        1        )            
In Equation (1), the H represents a channel matrix between transmitting and receiving ends, the x represents the transmitted symbol vector, the n represents an Additive White Gaussian Noise (AWGN) vector, the “hij” represents a channel response between an ith transmit antenna and a jth receive antenna, and the “di” represents a transmitted symbol from the ith transmit antenna and assumes an M-level Quadrature Amplitude Modulation (M-QAM) signal. Also, the “ni” represents an Additive White Gaussian Noise (AWGN) from an ith receive antenna and has power of σ2.
A Maximum Likelihood (ML) detection solution having an optimum performance in a system model given in Equation (1) is expressed in Equation (2) below:
                              x          ^                =                                                                              arg                  ⁢                                                                          ⁢                  min                                                                                                      x                  ∈                  C                                                              ⁢                                                                  r                -                                  H                  ·                  x                                                                    2                                              (        2        )            
In Equation (2), the “C” denotes a set of all possible candidate symbol vectors for a transmitted symbol vector (x), the r represents a received signal vector, the H represents a channel matrix between transmitting and receiving ends, and the x represents a transmitted symbol vector,
An optimal Log Likelihood Ratio (LLR) for a channel decoder is expressed through Equation (2) in Equation (3) below:
                                          L            ⁢                                                  ⁢            L            ⁢                                                  ⁢                          R              ⁡                              (                                  b                                      1                    ,                    i                                                  )                                              =                      log            ⁡                          (                                                                    ∑                                          c                      ∈                                              C                        1                        +                                                                                                                                            ⁢                                                            ∑                                                                        d                          2                                                ∈                        C                                                                                                                                  ⁢                                          exp                      (                                              -                                                                                                                                                                          r                                -                                                                                                      h                                    1                                                                    ⁢                                  c                                                                -                                                                                                      h                                    2                                                                    ⁢                                                                      d                                    2                                                                                                                                                                                      2                                                                                2                            ⁢                                                                                                                  ⁢                                                          σ                              2                                                                                                                          )                                                                                                            ∑                                          c                      ∈                                              C                        1                        -                                                                                                                                            ⁢                                                            ∑                                                                        d                          2                                                ∈                        C                                                                                                                                  ⁢                                          exp                      (                                              -                                                                                                                                                                          r                                -                                                                                                      h                                    1                                                                    ⁢                                  c                                                                -                                                                                                      h                                    2                                                                    ⁢                                                                      d                                    2                                                                                                                                                                                      2                                                                                2                            ⁢                                                                                                                  ⁢                                                          σ                              2                                                                                                                          )                                                                                  )                                      ⁢                                  ⁢                              L            ⁢                                                  ⁢            L            ⁢                                                  ⁢                          R              ⁡                              (                                  b                                      2                    ,                    i                                                  )                                              =                      log            ⁡                          (                                                                    ∑                                          c                      ∈                                              C                        1                        +                                                                                                                                            ⁢                                                            ∑                                                                        d                          1                                                ∈                        C                                                                                                                                  ⁢                                          exp                      (                                              -                                                                                                                                                                          r                                -                                                                                                      h                                    1                                                                    ⁢                                                                      d                                    1                                                                                                  -                                                                                                      h                                    2                                                                    ⁢                                  c                                                                                                                                                    2                                                                                2                            ⁢                                                                                                                  ⁢                                                          σ                              2                                                                                                                          )                                                                                                            ∑                                          c                      ∈                                              C                        1                        -                                                                                                                                            ⁢                                                            ∑                                                                        d                          1                                                ∈                        C                                                                                                                                  ⁢                                          exp                      (                                              -                                                                                                                                                                          r                                -                                                                                                      h                                    1                                                                    ⁢                                                                      d                                    1                                                                                                  -                                                                                                      h                                    2                                                                    ⁢                                  c                                                                                                                                                    2                                                                                2                            ⁢                                                                                                                  ⁢                                                          σ                              2                                                                                                                          )                                                                                  )                                                          (        3        )            
In Equation (3), the “bj,i” represents an ith bit of a transmitted symbol from a jth transmit antenna, the “Ci+” represents a set of dj having an ith bit of ‘+1’, and the “Ci−” represents a set of dj having an ith bit of ‘−1’. Also, the “hj” represents a jth column of a channel matrix (H), and the “σ2” represents power.
As expressed in Equation (3), LLR calculation in an ML receiver increases its complexity with exponential function with respect to a modulation order of a data symbol and the number of transmit antennas because there is a need to calculate a Euclidean distance for all possible transmitted symbol combinations. Thus, the ML receiver has a disadvantage that real-time realization is difficult if number of transmit antennas is large or the modulation order of the data symbol is high.
A solution to the aforementioned realization difficulty is a conventional Modified ML (MML) technique. The conventional MML technique cancels from a received signal each of the remaining symbol vectors transmissible from transmitting antennas excepting for a signal transmitted from any one transmit antenna, and then detects the excepted signal through slicing operation, thus being capable of maintaining the same performance as the ML detection technique while reducing a complexity to 1/M. For example, in a 64 Quadrature Amplitude Modulation (64QAM) scheme, the ML technique has to calculate a Euclidean distance for 642=4096 transmitted signal vectors, while the MML technique merely calculates a Euclidean distance only for 2×164=128 transmitted signal vectors. That is, the ML algorithm has to calculate a Euclidean distance for transmitted vectors of MNt (Nt: number of transmit antennas) number, while the MML algorithm calculates a Euclidean distance for transmitted vectors of MNt−1 number and detects a remaining single symbol through slicing operation.
The conventional MML technique is briefly described below. First, the MML technique cancels from a received signal possible influence of symbols transmitted from a first transmit antenna on all signals (d1=cmεC) as expressed in Equation (4) below:
                                          y            m                    =                                    r              -                                                h                  1                                ·                                  c                  m                                                      =                          r              -                                                [                                                                                                              h                          11                                                                                                                                                              h                          12                                                                                                      ]                                ·                                  c                  m                                                                    ,                  m          ∈                      {                          1              ,              2              ,              …              ⁢                                                          ,              M                        }                                              (        4        )            
In Equation (4), the “r” represents a received signal, the “h1” represents a channel vector between a first transmit antenna and a multiple receive antenna, and the “cm” represents a transmitted symbol vector, “h11” represents a channel response between an the first transmit antenna and a first receive antenna, and “h112 represents a channel response between an the first transmit antenna and a second receive antenna
Then, through a simple slicing operation, the MML technique determines a signal transmitted from a second transmit antenna among received signals from which the influence on the all signals (d1=cmεC) transmissible from the first transmit antenna is canceled. Additionally, the MML technique cancels influence on all signals transmissible from the second transmit antenna in the same manner and then, determines a signal transmitted from the first transmit antenna. After that, the MML technique calculates an LLR for determined transmitted vectors in a method such as Equation (5) below:
                                          L            ⁢                                                  ⁢            L            ⁢                                                  ⁢                          R              ⁡                              (                                  b                                      1                    ,                    i                                                  )                                              =                      log            ⁡                          (                                                                    ∑                                          c                      ∈                                              C                        1                        +                                                                                                                                            ⁢                                      exp                    (                                          -                                                                                                                                                              r                              -                                                                                                h                                  1                                                                ⁢                                c                                                            -                                                                                                h                                  2                                                                ⁢                                                                                                      d                                    2                                                                    ⁡                                                                      (                                    c                                    )                                                                                                                                                                                                            2                                                                          2                          ⁢                                                                                                          ⁢                                                      σ                            2                                                                                                                )                                                                                        ∑                                          c                      ∈                                              C                        1                        -                                                                                                                                            ⁢                                      exp                    (                                          -                                                                                                                                                              r                              -                                                                                                h                                  1                                                                ⁢                                c                                                            -                                                                                                h                                  2                                                                ⁢                                                                                                      d                                    2                                                                    ⁡                                                                      (                                    c                                    )                                                                                                                                                                                                            2                                                                          2                          ⁢                                                                                                          ⁢                                                      σ                            2                                                                                                                )                                                              )                                      ⁢                                  ⁢                              L            ⁢                                                  ⁢            L            ⁢                                                  ⁢                          R              ⁡                              (                                  b                                      2                    ,                    i                                                  )                                              =                      log            ⁡                          (                                                                    ∑                                          c                      ∈                                              C                        1                        +                                                                                                                                            ⁢                                      exp                    (                                          -                                                                                                                                                              r                              -                                                                                                h                                  1                                                                ⁢                                                                                                      d                                    1                                                                    ⁡                                                                      (                                    c                                    )                                                                                                                              -                                                                                                h                                  2                                                                ⁢                                c                                                                                                                                          2                                                                          2                          ⁢                                                                                                          ⁢                                                      σ                            2                                                                                                                )                                                                                        ∑                                          c                      ∈                                              C                        1                        -                                                                                                                                            ⁢                                      exp                    (                                          -                                                                                                                                                              r                              -                                                                                                h                                  1                                                                ⁢                                                                                                      d                                    1                                                                    ⁡                                                                      (                                    c                                    )                                                                                                                              -                                                                                                h                                  2                                                                ⁢                                c                                                                                                                                          2                                                                          2                          ⁢                                                                                                          ⁢                                                      σ                            2                                                                                                                )                                                              )                                                          (        5        )            
In Equation (5), the “bj,i” represents an ith bit of a symbol transmitted from a jth transmit antenna, the “Ci+” represents a set of dj having an ith bit of ‘+1’, and the “Ci−” represents a set of dj having an ith bit of ‘−1’. Also, the “hj” represents a jth column of a channel matrix (H), and the “σ2” represents power.
As such, the MML scheme can greatly reduce the complexity in realization when compared to a conventional scheme. However, as shown in Equations 4 and 5, when using a high modulation order, the MML technique requires a large number of complex multiplication operations and complex subtraction operations and thus, has a problem that a realization complexity is still high.